Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5470 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4845 | C2 | semidirect |
| 5. #4733 | C2 | semidirect |
| 6. #4699 | C2 | semidirect |
| 7. #4694 | C2 | semidirect |
| 8. #4693 | C2 | semidirect |
| 9. #4681 | C2 | semidirect |
| 44. #431 | D3 | semidirect |
| 219. C3 | #3210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| #5470 | 2 |
| C3×#431 | 2 |
| #4845 | 2 |
| #4733 | 2 |
| #4699 | 2 |
| #4694 | 2 |
| #4693 | 2 |
| #4681 | 2 |
| #3210 | 3 |